Structure of Atom MCQs

J.J. Thomson envisioned the atom as a uniformly positive sphere in which the negatively‑charged electrons are scattered like raisins.

Because the picture resembles a plum‑filled pudding, this description is popularly called the “plum pudding” model.

Thus the model referred to is Thomson’s model.

Neutron has no net electric charge, its constituent quarks’ charges cancel out.

Proton contains two up quarks (+2/3 each) and one down quark (‑1/3), giving +1 charge.

Electron carries a single negative charge (‑1).

Alpha particle is a helium nucleus (2 protons + 2 neutrons) with a +2 charge, so the neutral particle is the neutron.

Unit Conversion: Convert the wavelength from nanometers (nm) to meters (m):

λ = 600 nm = 600 × 10−9 m = 6 × 10−7

m

Substitution: Substitute the known values into the rearranged formula:

ν = (3 × 108

m/s) / (6 × 10−7 m)

Simplification:

ν = (3 / 6) × 108 − (−7)

ν = 0.5 × 1015 Hz = 5 × 1014 Hz

FINAL ANSWER

ν = 5.0 × 1014 Hz (or 500 THz)

Visible light corresponds to wavelengths roughly 400–700 nm.

In hydrogen, transitions that emit photons in this range end at the n=2 level.

These transitions are described by the Balmer formula (R_H(1/2²–1/n²)).

Hence the visible spectral series of hydrogen is the Balmer series.

Bohr radius a₀ = 0.529 Å for n = 1.

In Bohr model, radius rₙ = n²·a₀.

For the second orbit n = 2, r₂ = 2² × 0.529 Å = 4 × 0.529 Å.

Δx·Δp ≥ ħ/2 shows position–momentum uncertainty grows as the particle’s wavelength becomes comparable to its size.

For macroscopic bodies the de Broglie wavelength is extremely tiny, making Δx and Δp practically zero.

Thus the principle is noticeable only for microscopic particles. microscopic particles

Relative charge is a dimensionless number that expresses the electric charge of a subatomic

particle normalized against the magnitude of the elementary charge (e), where:

e ≈ 1.602 × 10−19 C

Since the proton carries exactly one elementary positive charge, its relative charge is evaluated as:

Relative Charge = +e / e = +1

Wavenumber is defined as the number of wave cycles in a unit length.

It is the reciprocal of the wavelength because wavelength is the distance for one cycle.

Thus wavenumber = 1 divided by λ, i.e., 1/λ.

In the photoelectric effect a photon must supply enough energy to free an electron from the metal.

That threshold energy is defined as the work function φ, the smallest energy needed to remove an electron.

Therefore the minimum energy required to eject an

Bohr radius a₀ = ħ²/(mₑ e²) = 0.529 × 10⁻¹⁰ m.

Convert to Å (1 Å = 10⁻¹⁰ m) gives a₀ = 0.529 Å.

Thus the radius of the first Bohr orbit of hydrogen is 0.529 Angstrom.

Uncertainty principle relates the spread in position (Δx) and momentum (Δp) of a particle.

Using Planck’s constant h, the reduced constant is ħ = h/2π, and the principle states Δx·Δp ≥ ħ/2.

Substituting ħ gives Δx·Δp ≥ (h/2π)/2 = h/4π.

Thus the correct mathematical form is delta x * delta p >= h/4pi

The azimuthal quantum number l determines the subshell type: l = 0 → s, l = 1 → p, l = 2 → d, l = 3 → f.

For the given value l = 2, the corresponding subshell is the d‑type.

Hence the subshell designation is d.

Alpha particles are positively charged and experience strong repulsion only when they come very close to the dense, positively charged nucleus.

The nucleus occupies an extremely small volume compared with the overall size of the atom.

Therefore, most alpha particles travel through regions where there is essentially no material to deflect them.

Hence most alpha particles passed straight through the foil because the atom is largely empty space.

Alpha particles mostly passed through the foil undeviated, showing most of the atom is empty space.

A few particles were sharply deflected, indicating a concentrated region of large positive charge.

The deflection angles required this region to be very small compared with the atomic size.

Thus Rutherford concluded the nucleus is small and positively charged.

Wavenumber (ṽ) is defined as the reciprocal of wavelength: ṽ = 1/λ.

Convert 500 nm to metres: 500 nm = 500 × 10⁻⁹ m = 5 × 10⁻⁷ m.

Take the reciprocal: 1/(5 × 10⁻⁷ m) = (1/5) × 10⁷ m⁻¹ = 0.2 × 10⁷ m

Transition to the ground level n=1 releases the largest energy among hydrogen series.

Using ΔE = hc/λ, the high ΔE gives λ < 400 nm.

Thus the Lyman series lies in the ultraviolet region.

Energy of the nth orbit is En = –13.6 eV / n² (hydrogen‑like atom).

The gap to the next level is ΔE = En+1 – En = 13.6 (1/n² – 1/(n+1)²).

Since 1/n² – 1/(n+1)² gets smaller for larger n, the spacing shrinks.

Thus the energy difference between successive orbits decreases.

Heisenberg’s principle states Δx·Δp ≥ ħ/2, so an electron’s position and momentum cannot be known simultaneously with arbitrary precision.

If an electron were in a definite fixed orbit, both its radius (position) and speed (momentum) would be exact, violating the principle.

Therefore the uncertainty principle rules out the existence of definite fixed orbits.

Bohr postulated that the electron’s orbital angular momentum is quantized.

He expressed this quantization as L = n·h/2π, where n is an integer (principal quantum number).

Thus each allowed orbit has angular momentum equal to an integral multiple of h/2π.

Hence the correct choice is h/2π

Protons determine the identity of an element.

The count of protons in the nucleus is defined as the atomic number.

Atomic number distinguishes one element from another.

Thus the number of protons in the nucleus of an atom is called its atomic number.